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Hence the value of x can be -19 or 21. Now, using the same x-5 can be -24 and 16. Out of the two only -24 is under the answer choices. Hence the answer is [C]. GMAT always considers the positive value of a square root i.e\sqrt{x^2} = |x| always. Please refer to the below threads if you have further queries:

I always thought maths is maths: as long as it's done without error, there is no right or wrong approach. Using \sqrt{400} +1 = -19 or +21 to derive the answer is the quickest and most direct approach (imho). I find that using roots is less prone to error because there are fewer steps and less to write down - but I doubt everyone is wired the same.

GMAT does not test approaches, only answers.

It seems to me the \sqrt{25} = +5 is a house rule when writing questions, and I'm fine with any rules until those rules change without notice.

I always thought maths is maths: as long as it's done without error, there is no right or wrong approach. Using \sqrt{400} +1 = -19 or +21 to derive the answer is the quickest and most direct approach (imho). I find that using roots is less prone to error because there are fewer steps and less to write down - but I doubt everyone is wired the same.

GMAT does not test approaches, only answers.

My friend, the reason that I mentioned that your method is not the correct way is that, when GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root. In such a case \sqrt{400} would only be 20 and not {20,-20}. The solution to the equation \sqrt{x^2} = |x| i.e. the positive value only.

Now the method used by you is not wrong, but clearly the approach is not suited for GMAT-based questions. I am just echoing the concept which has been time and again elaborated very elegantly by several members in this community. If you do end up using the same concept over a different and rather complicated question, I would certainly wont want you to get it wrong just because of this. I'd request you to go through some of the reading material available at the forum, and some wonderful posts by Bunuel. I have mentioned some threads already in my previous post. I understand that end result is important, but the way we reach it is even more critical As it is said, The path walked is more important than the destination.- Corinthians 9:24 -